Advertisements
Advertisements
प्रश्न
Find the middle term of the AP. 95, 86, 77, ........, – 247.
Advertisements
उत्तर
Given A.P. is 95, 86, 77, ....., – 247
Here, a = 95, d = 86 – 95 = – 9
Let the A.P. has n terms.
Then, an = a + (n – 1)d
⇒ – 247 = 95 + (n – 1) (– 9)
⇒ – 247 = 95 – 9n + 9
⇒ – 247 = 104 – 9n
⇒ 9n = 104 + 247
⇒ 9n = 351
⇒ n = 39
Thus, the given A.P. has 39 terms.
Now, Middle term = `[1/2 (39 + 1)]^(th)` term
= `[1/2 (40)]^(th)` term
= 20th term
a20 = a + 19d
= 95 + 19 (– 9)
= 95 – 171
= – 76
As a result, the specified A.P.'s middle term is – 76.
APPEARS IN
संबंधित प्रश्न
Find the sum of the following APs:
0.6, 1.7, 2.8, ... to 100 terms.
How many terms of the AP. 9, 17, 25 … must be taken to give a sum of 636?
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato and other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line.
A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
[Hint: to pick up the first potato and the second potato, the total distance (in metres) run by a competitor is 2 × 5 + 2 × (5 + 3)]
Find the sum of the following arithmetic progressions:
–26, –24, –22,... to 36 terms
Find the sum of all natural numbers between 1 and 100, which are divisible by 3.
The 4th term of an AP is 11. The sum of the 5th and 7th terms of this AP is 34. Find its common difference.
If the pth term of an AP is q and its qth term is p then show that its (p + q)th term is zero.
In an A.P. sum of three consecutive terms is 27 and their product is 504, find the terms.
(Assume that three consecutive terms in A.P. are a – d, a, a + d).
Find four consecutive terms in an A.P. whose sum is 12 and sum of 3rd and 4th term is 14.
(Assume the four consecutive terms in A.P. are a – d, a, a + d, a +2d)
The sum of third and seventh term of an A. P. is 6 and their product is 8. Find the first term and the common difference of the A. P.
Ramkali would need ₹1800 for admission fee and books etc., for her daughter to start going to school from next year. She saved ₹ 50 in the first month of this year and increased her monthly saving by ₹ 20. After a year, how much money will she save? Will she be able to fulfil her dream of sending her daughter to school?
If Sn denotes the sum of the first n terms of an A.P., prove that S30 = 3(S20 – S10).
If the sums of n terms of two arithmetic progressions are in the ratio \[\frac{3n + 5}{5n - 7}\] , then their nth terms are in the ratio
If 18, a, b, −3 are in A.P., the a + b =
The common difference of the A.P. is \[\frac{1}{2q}, \frac{1 - 2q}{2q}, \frac{1 - 4q}{2q}, . . .\] is
Q.10
Find the value of x, when in the A.P. given below 2 + 6 + 10 + ... + x = 1800.
In an A.P. a = 2 and d = 3, then find S12.
The sum of first ten natural number is ______.
The nth term of an A.P. is 6n + 4. The sum of its first 2 terms is ______.
